Selectividad / EvAU (Spain) · Mathematics

Linear Algebra, Calculus, Geometry and Probability

40 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 40 questions

What is the rank of the matrix $A = (1236)$ ?
What is the limit $lim_{x \to 0} \frac{s i n ( 4 x )}{2 x}$ ?
What is the determinant of the matrix $M = 130012241$ ?
What is the derivative of $f (x) = x^{3} ln (x)$ at $x = 1$ ?
For which value of parameter $m$ is the system $⎩ ⎨ ⎧ x + y + z = 1 2 x + 3 y + m z = 3 x + 2 y + 3 z = 2$ incompatible (no solution)?
What is the antiderivative $\int \frac{1}{2 x + 3} d x$ ?
What is the distance from the point $P (2, - 1, 3)$ to the plane $π : 2 x - 2 y + z - 1 = 0$ ?
What is the area of the finite region enclosed by $y = x^{2} - 2 x$ and the line $y = x$ ?
What is the value of the definite integral $\int_{0}^{2} (3 x^{2} - 2 x + 1) d x$ ?
If events $A$ and $B$ are independent with $P (A) = 0.6$ and $P (B) = 0.3$ , what is $P (A \cup B)$ ?
What is the volume of the parallelepiped defined by vectors $u = (1, 0, 2)$ , $v = (0, 3, 1)$ , and $w = (2, 1, 0)$ ?
What are the vertical asymptotes of the rational function $f (x) = \frac{x + 2}{x ^{2} - 4}$ ?
What is the derivative of $f (x) = arctan (2 x)$ ?
What is the point on the plane $π : x + y + z = 6$ closest to the origin $(0, 0, 0)$ ?
What is the value of $\int_{0}^{1} x e^{- x} d x$ ?
What are the values of $a$ and $b$ that make $f (x) = {a x^{2} + b x 2 x + 1 x \leq 1 x > 1$ differentiable at $x = 1$ ?
What is the inverse matrix of $A = (2005)$ ?
In a normal distribution $X \sim N (100, 15)$ , what is the z-score corresponding to $X = 130$ ?
What is the line of intersection of planes $π_{1} : x + y - z = 1$ and $π_{2} : 2 x - y + z = 2$ ?
What is the local maximum of $f (x) = - x^{2} + 6 x - 5$ ?
What is the cross product $i \times j$ in $R^{3}$ ?
What is the slope of the normal line to $y = x^{2}$ at the point $(1, 1)$ ?
What is the integral $\int \frac{2 x + 1}{x ^{2} + x - 2} d x$ ?
If a fair coin is tossed 4 times, what is the probability of getting exactly 3 heads?
What is the solution to the matrix equation $A X = B$ when $A = (1002)$ and $B = (34)$ ?
What is the inflection point of the cubic curve $y = x^{3} - 6 x^{2} + 9 x + 1$ ?
What is the distance between the parallel planes $π_{1} : 2 x - y + 2 z = 4$ and $π_{2} : 2 x - y + 2 z = 10$ ?
What is the value of $lim_{x \to 1} \frac{x ^{3} - 1}{x ^{2} - 1}$ ?
What is the probability of obtaining a sum of 7 when rolling two standard six-sided dice?
What is the value of the integral $\int_{1}^{e} ln (x) d x$ ?
For which value of $k$ are vectors $u = (2, k, 1)$ and $v = (3, - 2, 4)$ orthogonal?
What is the maximum value of $f (x) = x e^{- x}$ for $x \geq 0$ ?
What is the determinant of the $2 \times 2$ matrix $B = (42 - 1 3)$ ?
What is the derivative of $f (x) = x^{2} + 9$ at $x = 4$ ?
What is the area bounded by the curve $y = cos (x)$ , the x-axis, and the lines $x = 0$ and $x = π$ ?
What is the equation of the tangent line to $y = e^{2 x}$ at $x = 0$ ?
What is the mean $μ$ of a binomial distribution $B (50, 0.2)$ ?
What is the value of $lim_{x \to 0} \frac{x - s i n ( x )}{x ^{3}}$ ?
What is the distance between point $A (1, 2, 3)$ and point $B (4, 2, - 1)$ ?
What is the value of the parameter $a$ for which the matrix $C = (1 a a 4)$ is NOT invertible?

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